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Herz-Schur multipliers of dynamical systems

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OAS - Operator algebras: subfactors and their applications

Herz-Schur multipliers of a locally compact group, introduced by Haagerup and de Canniere in 1985, have been instrumental in operator algebra theory in a variety of contexts, in particular in the study of approximation properties of group operator algebras. They can be viewed as the invariant part of the Schur multipliers – a class of maps on B(H) with another long list of applications, e.g. in perturbation theory of linear operators. In this talk, which is based on a joint work with A. McKee and L. Turowska, I will introduce operator-valued Schur and Herz-Schur multipliers of arbitrary locally compact groups. The latter give rise to natural maps on C*- and von Neumann algebra crossed products. I will present a characterisation of operator-valued Herz-Schur multipliers as the invariant part of the operator-valued Schur multipliers, and will discuss various special cases which highlight the generality of this class of maps and their potential usefulness in subsequent research.

This talk is part of the Isaac Newton Institute Seminar Series series.

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